Hedstrom number, abbreviated as He, a dimensionless number, is used in fluid dynamics to characterize the relative importance of viscous forces to inertial forces in a fluid flow. The Hedström number helps determine whether viscous effects or inertial effects dominate in a fluid flow. Its interpretation is similar to the Reynolds number, which is another dimensionless parameter used in fluid dynamics. The key differences between the Hedström number and the Reynolds number are the choice of characteristic velocity and the absence of density in the Hedström number.
Hedstrom Number Interpretation
- Low Hedstrom Number (He << 1) - Viscous forces dominate over the yield stress effects. The fluid behaves more like a regular viscous fluid (closer to Newtonian), and the yield stress doesn’t play a huge role in resisting flow. Flow starts relatively easily, and the behavior is governed more by viscosity than the initial "stiffness" of the fluid.
- High Hedstrom Number (He >> 1) - The yield stress becomes much more significant compared to viscous forces. This means the fluid resists flowing until a substantial pressure or force is applied to overcome the yield stress. In a pipe, for instance, you might see a solid-like "plug" of fluid in the center that doesn’t shear until the stress exceeds τ0, surrounded by a sheared layer near the walls.
- Intermediate Hedstrom Number (He ≈ 1) - This is a transitional regime where both yield stress and viscosity contribute noticeably to the flow behavior. The fluid might start to move but with a mix of plug-like and sheared regions, depending on the applied stress.
In pipe flow, for example, a high Hedstrom Number indicates that you’ll need a lot more pressure to get the fluid moving, and once it does, the flow might have a distinct "core" that moves as a solid lump. A low Hedstrom Number suggests the fluid flows more smoothly with less resistance from the yield stress.It’s often used alongside the Reynolds Number (which compares inertia to viscosity) to fully describe non-Newtonian flow regimes. For Bingham fluids, the Hedstrom Number helps engineers design pumps, pipelines, or mixers by predicting how much force is needed to initiate and sustain flow.
Hedstrom Number formula |
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| \( He \;=\; \dfrac{ \left(\rho \cdot d^2\right) \cdot \tau }{ \mu^2 } \) | ||
| Symbol | English | Metric |
| \( He \) = Hedstrom Number | \(dimensionless\) | \(dimensionless\) |
| \( \rho \) (Greek symbol rho) = Fluid Mass Density | \(lbm\;/\;ft^3\) | \(kg\;/\;m^3\) |
| \( d \) = Pipe Inside Diameter | \(in^2\) | \(mm^2\) |
| \( \tau \) (Greek symbol tau) = Pipe Yield Point | \(in\) | \(mm\) |
| \( \mu \) (Greek symbol mu) = Fluid Dynamic Viscosity | \(lbf-sec\;/\;ft^2\) | \( Pa-s \) |
